To verify that this novel architecture works well on real-world graph classification datasets, following [1]} we use three bioinformatics datasets (MUTAG, PTC, PROTEINS) and two social network datasets (IMDB-BINARY and IMDB-MULTI) [2]}. As graphs in these datasets only have 10s of nodes per graph on average, we also include one large-graph protein dataset (DD) [3]} and one large-graph social dataset (REDDIT-BINARY) [2]}. In these datasets, graphs have hundreds of nodes on average and the largest graphs have thousands of nodes (Appendix ).
We compare our model to GIN, which has maximal 1-WL expressive power achievable by a standard message-passing GNN [5]}, and more expressive GNN architectures, which do not require pre-computed features [1]}, [7]}, [8]}, [9]}. As you can see in Table REF  our novel approach always outperforms at least half of the more expressive baselines. Even the model that uses just a single agent matches the performance of GIN, even though in this case the agent cannot visit the whole graph, as for these experiments we only consider \(\ell \in \lbrace 8, 16\rbrace \)  (Appendix ) and using only one agent reduces expressiveness. Naturally, 1-AgnetNet performance deteriorates on the large graphs, while AgentNet does very well. The higher-order methods cannot even train on these large graphs on a 24GB GPU. To train the ESAN and DropGIN models on them we have to only use \(5\%\)  of the usual \(n\)  different versions of the same graph [7]}. For DropGIN, this results in a loss of accuracy. While ESAN performs well in this scenario, it requires lengthy pre-processing and over 120GB of main memory to load the pre-processed dataset (original datasets are \(<150\) MB), which can become prohibitive if we need to test even larger graphs.
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